Question

Suppose that $3<a<4$ and $4<b<5$. Find all possible values of:
$a-b$

Answer 1

Finding the possible values of $a-b$:

Given, $3<a<4$ and $4<b<5$.

If $4<b<5$, then $-4>-b>-5$ or $-5<-b<-4$.

So, we can write,

$$\begin{gathered} \Rightarrow 3<a<4 \\ \Rightarrow 3-5<a-b<4-4 \\ \Rightarrow -2<a-b<0 \end{gathered}$$

Hence, the possible value of $a-b$ is $-2<a-b<0$.